An importance sampling algorithm for generating exact eigenstates of the nuclear Hamiltonian

We endow a recently devised algorithm for generating exact eigensolutions of large matrices with an importance sampling, which is in control of the extent and accuracy of the truncation of their dimensions. We made several tests on typical nuclei using a correlated basis obtained from partitioning the shell model space. The sampling so implemented allows not only for a substantial reduction of the shell model space but also for an extrapolation to exact eigenvalues and E2 strengths.